First Lady Chirlane McCray has taken on a co-governing role in City Hall with her husband, Mayor de Blasio, that appears to have surpassed even that of his top deputy.

The unprecedented, unsalaried and, by all accounts, unofficial advisory post was on full display Monday in the announcement of Houston schools chief Richard Carranza as the city’s new schools chancellor.

Hizzoner not only publicly praised his wife for her role in the selection process — he mentioned her before First Deputy Mayor Dean Fuleihan.

“I want to thank Chirlane for the many, many hours she has put in this effort,” de Blasio said in a statement before adding, “I want to thank First Deputy Mayor Dean Fuleihan, as well. The three of us acted as a team.’’

McCray, City Hall revealed, also sat in on meetings all weekend between her husband and his top aides discussing the appointment. And the first lady was there when de Blasio made Carranza an official offer.

A quote from McCray was included in the press release, too.

“I look forward to working closely with [Carranza] to help all of the inner cities’ children and their families,” she said.

But political observers say that there’s more to McCray’s input in official city business than meets the eye — that it is a bid to elevate her political standing for a possible run for office herself.

“There’s a concerted effort to get her as much exposure as possible,” said a source familiar with McCray’s role at City Hall.

“There’s a clear understanding . . . that these are joint announcements, and Chirlane is going to have a presence and a voice every time one of these appointments is being made.”

Democratic political consultant George Arzt noted “rumors are already swirling” about McCray running for political office.

“She’s very powerful now, and I think she’ll become even more visible,” Arzt said.

“Certainly, there has never been anyone like her in city government.”

When reporters started questioning McCray’s involvement after the Carranza rollout Monday, mayoral press secretary Eric Phillips testily tweeted back: “She’s not only at all the big announcements. She’s involved in all the big decisions.”

And on NY1 later, de Blasio dismissed criticism of McCray’s involvement in his administration as “the most idiotic thing I ever heard in my life.

“It smacks of sexism,” he added angrily.

Luiz Rampelotto/Sipa USA

But behind the scenes, the mayor and his aides have been laying the groundwork for ­McCray’s ascension for some time. De Blasio has been effusive in his admiration for — and professional reliance on — his wife since before he even took office.

Calling her “my closest confidante” and “No. 1 adviser,” the mayor gave McCray, who is legally barred from drawing a salary, a full-time staff of five to work out of both Gracie Mansion and City Hall.

He also has her regularly sit in on policy and staff meetings and handed her official posts, from chair of the Mayor’s Fund to Advance New York City to the head of a major mental-health initiative that provides services in the most needy neighborhoods.

“The first lady is obviously a top representative of the city, overseeing programs critical to our mental-health and anti-addiction campaigns,” said mayoral spokeswoman Freddi Goldstein.

De Blasio told reporters at the time that McCray “joined” him “in feeling great enthusiasm as we went through this [hiring] process,” and that “she is going to be working very, very closely with our new deputy mayor.”

Administration officials later claimed the wording of the press release was unintentional and updated it online.

“Certainly there has never been anyone like [McCray] in city government.”

- George Arzt

But a review of public records also shows McCray has been upping her involvement in official city business.

In de Blasio’s first two years in office, McCray participated in 82 staff meetings, phone calls and public events with her hubby, the records show.

Over the mayor’s second two years, she more than quadrupled her participation in internal meetings and public events to 343.

McCray has also taken 10 solo trips out of the city since May 2015, including six billed to taxpayers — and a pair in just the first two months of 2018 alone. The solo jaunts included four trips to Washington, DC, three to Atlanta, and visits to Chicago, Massachusetts and Italy. She also has been on 11 business trips with the mayor. Of her solo business trips, three occurred in the past four months alone.

McCray’s excursions have included speaking engagements, award ceremonies and sit-downs with former presidential First Ladies Hillary Clinton and Rosalyn Carter and other high-profile elected officials.

The goal is to get her as much exposure as possible without adding the burden of intense media scrutiny, said the source familiar with the situation.

“She doesn’t do interviews and doesn’t take questions at press conferences,” the source said.

“There’s a concerted effort to get her as much exposure as possible — without the heavy lift.” Her experience includes overseeing the administration’s $850 million Thrive New York mental-health program, as well as the Mayor’s Fund to Advance New York, a nonprofit that raises money for City Hall pet projects.

Emails obtained by The Post show that while building her Gracie Mansion résumé, McCray consulted in early 2015 with de Blasio’s main campaign pollster, Anna Greenberg, of Greenberg Quinlan Rosner Research, in Washington, DC.

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“I spoke with [one of your aides] today, and she talked about the initiative you will undertake in 2015 centered around mental health, domestic violence and [children ages] 0 to 3,” Greenberg wrote in an e-mail to McCray in December 2014.

“I would be very happy to talk to you about your plans and how it fits into what I see in the polling in the city and around the country.”

McCray wrote back, “I would be so grateful to have some of your brain power.”

De Blasio campaign officials said Greenberg didn’t conduct specific polling for McCray but was referring in the e-mail to her general polling knowledge — which, they were quick to add, she shared at no cost.

Arzt said he believes McCray would be a “formidable” candidate for several political seats.

He said he could see her running to replace Brooklyn Borough President Eric Adams or Councilman Brad Lander, who represents Park Slope, where McCray and the mayor lived before Gracie Mansion and still own a home. Both men’s terms expire in 2021.

McCray started the buzz herself in November — days after de Blasio won a second term — by telling Cosmopolitan magazine that she would “consider” seeking elected office someday, just not for mayor.

“We need women to run,” she said. “I encourage women to run. So I can’t rule it out myself.”

McCray is a far cry from previous mayors’ spouses.

Divorced former Mayor Bloomberg dated longtime girlfriend Diana Taylor throughout his tenure, but while she is an accomplished banking expert, she kept her public involvement in her boyfriend’s position limited to social events and the campaign trail.

Mayor Dinkins’ wife, Joyce, stayed out of the limelight for the most part, too, while bachelor Mayor Koch fought to keep rumors that he was gay at bay by socially squiring around former Miss America Bess Myerson.

The closest, most recent comparison would be to Donna Hanover, who was Mayor Rudy Giuliani’s wife in the 1990s.

Hanover had a staff of four and office space in Gracie Mansion, but she focused on charity and social issues and wasn’t involved in personnel decisions or policy.

By comparison, de Blasio “is always running stuff by [McCray], and staff are always checking to make sure she’s been consulted,” said the knowledgeable source.

“It’s very much a given that the administration is run by that partnership.”